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Sorry, no picture. Just a civ noob trying to get better. Here's the setup - I'm playing a Standard map (large Islands) with 6 civs & 10 city-states. Civs were Sweden (me), Russia, Polynesia, America, Egypt, and Inca. I spawn next to Russia and had a mini cold war going the entire game. Polynesia forward settles Russia and takes a natural wonder (Mt. Keliah). Polynesia and I have been friends from the start. Russia declares war on Polynesia and takes the Polynesian city with Mt. Keliah. I declare war on Russia and take back the Polynesian city and liberate it back to Polynesia. Russia makes peace with me the turn after I liberate the city. The next turn Russia denounces me - no biggie since we have been doing that all game. However, Polynesia, the same civ I just saved their city for, denounces me as well. I think Russia and Polynesia may have become friends after they sued for peace, but I don't remember.

So why is it that Polynesia, who has been friends with me all game and I just gave them back their city denounce me? Would it have anything to do with me shooting down the Polynesia resolutions in the world congress to ban my luxuries the last 2 times?

Civ AI is backstabbing and illogical, there is no such thing as a lasting friendship with them. They weight things you do unintentionally, like ally with a city state, as being out to get them. If they are your neighbor, they will always covet your lands. The AI treats your wrongs and their own greed as the same thing, just red modifiers that make them hate you.

Sounds a bit like a human player, doesn't it? Don't you get pissed when someone takes your city state? Don't you backstab the AI? Don't you eye up the AIs lands? Even if you personally don't, you have to realize that most players do act that way.

Basically, if a civ A denounces civ B then other civs that are friendly with civ A, but less friendly with civ B, will denounce civ B as well.

So basically, Russia denounced you, and Polynesia is friendly with Russia and likes them better than they like you, so they denounce you to.

Why Polynesia liked Russia better than you, I don't know, it depends on the diplomacy math (which can be a little skewed). Voting against their resolutions could be big minuses, Russia might have trade routes with Polynesia and you don't, maybe Polynesia and Russia were the same ideology (and you weren't?). The math, and the weight given to different diplo options, can be a little screwy sometimes.

Ok, thanks. I was just shocked that not 2 turns after I liberate a city to a civ that had been friends with me the whole game, though a bit less so I guess since I didn't let my luxs get banned, they denounced me. Is voting down another civs resolutions really that bad for skewing things diplomatically?

It's a bit strange, I'm not sure whether they have to actually dislike you, or if they just have to like Russia better than you to denounce when Russia denounces

It doesn't look that bad, not sure what happened. At the bottom of this page you can see all the good and bad modifiers and their values. If you hover over their name in the diplomacy menu, it will show you good and bad modifiers.

Also, Polynesia (and Catherine) have a pretty high denounce willingness, according to http://civdata.com/ so he denounces pretty easily.